Let $Z$ denote the set of integers. Then match the items in list-$\mathrm{I}$, with those of the items in List-$\mathrm{II}$

	List- $\mathrm{I}$		List- $\mathrm{II}$
$\left(\mathrm{A}\right)$	${\sin }^{-1}\left(\frac{2\sqrt{2}}{3}\right)+{\sin }^{-1}\frac{1}{3}$	$\left(\mathrm{I}\right)$	$k\pi \pm {\left(-1\right)}^k\frac{\pi }{6}, k\in Z$
$\left(\mathrm{B}\right)$	${\sin }^{-1}\left(\frac{{\left(-1\right)}^n}{2}\right), n\in Z$	$\left(\mathrm{II}\right)$	$k\pi \pm 1, k\in Z$
$\left(\mathrm{C}\right)$	${\tan }^{-1}\left(\sec \frac{\pi }{4}+\tan \frac{\pi }{4}\right)$	$\left(\mathrm{III}\right)$	$\frac{3}{2}$
$\left(\mathrm{D}\right)$	${\sin }^{-1}\left|\sin x\right|=\sqrt{{\sin }^{-1}\left|\sin x\right|}\Rightarrow x\in$	$\left(\mathrm{IV}\right)$	$\frac{3\pi }{8}$
		$\left(\mathrm{V}\right)$	$\frac{\pi }{2}$

The correct match is

• A

  $\begin{array}{cccc}\left(\mathrm{A}\right)& \left(\mathrm{B}\right)& \left(\mathrm{C}\right)& \left(\mathrm{D}\right)\\ \mathrm{V}& \mathrm{I}& \mathrm{III}& \mathrm{II}\end{array}$
• B

  $\begin{array}{cccc}\left(\mathrm{A}\right)& \left(\mathrm{B}\right)& \left(\mathrm{C}\right)& \left(\mathrm{D}\right)\\ \mathrm{IV}& \mathrm{II}& \mathrm{V}& \mathrm{I}\end{array}$
• Correct answer
  C

  $\begin{array}{cccc}\left(\mathrm{A}\right)& \left(\mathrm{B}\right)& \left(\mathrm{C}\right)& \left(\mathrm{D}\right)\\ \mathrm{V}& \mathrm{I}& \mathrm{IV}& \mathrm{II}\end{array}$
• D

  $\begin{array}{cccc}\left(\mathrm{A}\right)& \left(\mathrm{B}\right)& \left(\mathrm{C}\right)& \left(\mathrm{D}\right)\\ \mathrm{IV}& \mathrm{II}& \mathrm{V}& \mathrm{III}\end{array}$

Hence, the correct answer is option: 'C'.